My U.S. patent application Ser. No. 518,782 discloses a baseball bat or the like formed of a tube having an outer layer of wood veneer overlying an inner layer of fiber reinforced resin, with the two layers being impregnated with and bonded together with cured resin. Such bats have the desirable aesthetic appearance of solid wood bats, are much less susceptible to breakage in use than solid wood bats and can be designed to emulate the performance of either solid wood bats or exceed the performance of the livelier aluminum bats with larger sweet-spots. The present invention is directed toward improved versions of such bats and to methods of making the bats.